Question

1. determine the value of x.

a. ( x = 32^{circ} ) b. ( x = 180^{circ} )
c. ( x = 74^{circ} ) d. ( x = 148^{circ} )

Explanation:

Step1: Use the property of isosceles triangle

Since two sides of the triangle are equal (marked with the same tick), the triangle is isosceles. In an isosceles triangle, the base - angles are equal. So the angle opposite to the side with the same mark as the side adjacent to the \(32^{\circ}\) angle is also \(32^{\circ}\).

Step2: Use the angle - sum property of a triangle

The sum of angles in a triangle is \(180^{\circ}\). Let \(x\) be the unknown angle. Then \(x + 32^{\circ}+32^{\circ}=180^{\circ}\).

$$x=180^{\circ}-(32^{\circ} + 32^{\circ})$$

$$x = 180^{\circ}-64^{\circ}$$

$$x=74^{\circ}$$

Answer:

C. \(x = 74^{\circ}\)